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Summer 1997 Grundgesetze der Arithmetik I §§29‒32
Richard G. Heck Jnr.
Notre Dame J. Formal Logic 38(3): 437-474 (Summer 1997). DOI: 10.1305/ndjfl/1039700749


Frege's intention in section 31 of Grundgesetze is to show that every well-formed expression in his formal system denotes. But it has been obscure why he wants to do this and how he intends to do it. It is argued here that, in large part, Frege's purpose is to show that the smooth breathing, from which names of value-ranges are formed, denotes; that his proof that his other primitive expressions denote is sound and anticipates Tarski's theory of truth; and that the proof that the smooth breathing denotes, while flawed, rests upon an idea now familiar from the completeness proof for first-order logic. The main work of the paper consists in defending a new understanding of the semantics Frege offers for the quantifiers: one which is objectual, but which does not make use of the notion of an assignment to a free variable.


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Richard G. Heck Jnr.. "Grundgesetze der Arithmetik I §§29‒32." Notre Dame J. Formal Logic 38 (3) 437 - 474, Summer 1997.


Published: Summer 1997
First available in Project Euclid: 12 December 2002

zbMATH: 0915.03005
MathSciNet: MR1624970
Digital Object Identifier: 10.1305/ndjfl/1039700749

Primary: 03-03
Secondary: 03A05

Rights: Copyright © 1997 University of Notre Dame


Vol.38 • No. 3 • Summer 1997
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